Central Pattern Generator Incorporating the Actuator Dynamics for a Hexapod Robot
We proposed the use of a Toda-Rayleigh ring as a
central pattern generator (CPG) for controlling hexapodal robots. We
show that the ring composed of six Toda-Rayleigh units coupled to
the limb actuators reproduces the most common hexapodal gaits. We
provide an electrical circuit implementation of the CPG and test our
theoretical results obtaining fixed gaits. Then we propose a method
of incorporation of the actuator (motor) dynamics in the CPG. With
this approach we close the loop CPG – environment – CPG, thus
obtaining a decentralized model for the leg control that does not
require higher level intervention to the CPG during locomotion in
a nonhomogeneous environments. The gaits generated by the novel
CPG are not fixed, but adapt to the current robot bahvior.
[1] E. Kandel, J. Schwartz, and T. Jessell, Principles of Neural Science.
Kandel and Schwartz Ed., Elsevier 1991.
[2] C. A. Wiersma (ed.) Invertebrate nervous systems. Univ. Chicago Press
1968.
[3] H. Cruse, "What mechanisms coordinate leg movement in working
arthropods?", Trends in NeuroScience, vol. 13, pp. 15-21, 1990.
[4] M. Golubitsky, I. Stewart, P.-L Buono, and J. J. Collins, "Symmetry in
locomotor central pattern generators and animal gaits", Nature, vol. 401,
pp. 693-695, 1999.
[5] H. Cruse, T. Kindermann, M. Schumm, J. Dean, and J. Schmitz,
"Walknet - a biologically inspired network to control six-legged walking",
Neural Networks, vol. 11, pp. 1435, 1998.
[6] P. Arena, L. Fortuna, and M. Branciforte, "Reaction-diffusion CNN
Algorithms to Generate Artificial Locomotion", IEEE Trans. Circuits
Systems I, vol. 46, pp. 253, 1999.
[7] W. Y. Yiang, G. Schooner, and J.A.S. Kelso, "A synergetic theory of
quadrupedal gaits and gait transition", J. Theor. Biol. vol. 142, pp. 359-
391, 1990.
[8] J. J. Collins and I. Stewart, "Coupled nonlinear oscillators and the
symmetries of animal gaits" Nonlinear Science, vol. 3, pp. 349-392,
1993.
[9] J. J. Collins and I. Stewart, "Hexapodal gaits and coupled nonlinear
oscillator models". Biological Cybernetics vol. 68, pp. 287-298, 1993.
[10] J. J. Collins and I. Stewart, "A group-theoretic approach to rings of
coupled biological oscillators", Biological Cybernetics vol. 71, pp. 95-
103, 1994.
[11] M. Golubitsky, I. Stewart, P. L. Buono, and J. J. Collins, "A modular
network for legged locomotion", Physica D vol. 115, pp. 56-72, 1998.
[12] J. W. Rayleigh, The Theory of Sound 2nd ed., Dover N.Y., 1945.
[13] M. Toda, Theory of Nonlinear Lattices, Springer Berlin, 1981.
[14] M. Toda, Nonlinear Waves and Solitons, Kluwer Dordrecht, 1983.
[15] V. A. Makarov, W. Ebeling, and M. G. Velarde, "Soliton-like waves
on dissipative Toda lattices", Int. J. Bifurcation and Chaos vol. 10, pp.
1075-1089, 2000.
[16] V. A. Makarov, E. Del Rio, W. Ebeling, and M. G. Velarde, "Dissipative
Toda-Rayleigh lattice and its oscillatory modes", Physical Review E vol.
64, pp. 036601-36615, 2001.
[17] E. Del Rio, V. A. Makarov, M. G. Velarde, and W. Ebeling, "Mode
transitions and wave propagation in a driven-dissipative Toda-Rayleigh
ring", Physical Review E vol. 67, pp. 056208-056217, 2003.
[18] S. Still, K. Hepp, and R. J. Douglas, "Neuromorphic walking gait
control", IEEE Trans. Neural Netw. vol 17, pp. 496-508, 2006.
[19] V. A. Makarov, M. G. Velarde, A. Chetverikov, and W. Ebeling,
"Anharmonicity and its significance to non-Ohmic electric conduction",
Physical Review E, vol. 73, pp. 066626-066612, 2006.
[20] Yu. A. Kuznetsov, Elements of Applied Bifurcation Theory, Springer-
Verlag, Berlin, 1995.
[21] A. C. Singer and A. V. Oppenheim, "Circuit implementation of soliton
systems", Int. J. Bifurcation Chaos vol. 9, pp. 571, 1999.
[22] N. Islam, J. P. Singh, and K. Steiglitz, "Soliton phase shifts in a
dissipative lattice", J. Appl. Phys. vol. 62, pp. 689-693, 1987.
[1] E. Kandel, J. Schwartz, and T. Jessell, Principles of Neural Science.
Kandel and Schwartz Ed., Elsevier 1991.
[2] C. A. Wiersma (ed.) Invertebrate nervous systems. Univ. Chicago Press
1968.
[3] H. Cruse, "What mechanisms coordinate leg movement in working
arthropods?", Trends in NeuroScience, vol. 13, pp. 15-21, 1990.
[4] M. Golubitsky, I. Stewart, P.-L Buono, and J. J. Collins, "Symmetry in
locomotor central pattern generators and animal gaits", Nature, vol. 401,
pp. 693-695, 1999.
[5] H. Cruse, T. Kindermann, M. Schumm, J. Dean, and J. Schmitz,
"Walknet - a biologically inspired network to control six-legged walking",
Neural Networks, vol. 11, pp. 1435, 1998.
[6] P. Arena, L. Fortuna, and M. Branciforte, "Reaction-diffusion CNN
Algorithms to Generate Artificial Locomotion", IEEE Trans. Circuits
Systems I, vol. 46, pp. 253, 1999.
[7] W. Y. Yiang, G. Schooner, and J.A.S. Kelso, "A synergetic theory of
quadrupedal gaits and gait transition", J. Theor. Biol. vol. 142, pp. 359-
391, 1990.
[8] J. J. Collins and I. Stewart, "Coupled nonlinear oscillators and the
symmetries of animal gaits" Nonlinear Science, vol. 3, pp. 349-392,
1993.
[9] J. J. Collins and I. Stewart, "Hexapodal gaits and coupled nonlinear
oscillator models". Biological Cybernetics vol. 68, pp. 287-298, 1993.
[10] J. J. Collins and I. Stewart, "A group-theoretic approach to rings of
coupled biological oscillators", Biological Cybernetics vol. 71, pp. 95-
103, 1994.
[11] M. Golubitsky, I. Stewart, P. L. Buono, and J. J. Collins, "A modular
network for legged locomotion", Physica D vol. 115, pp. 56-72, 1998.
[12] J. W. Rayleigh, The Theory of Sound 2nd ed., Dover N.Y., 1945.
[13] M. Toda, Theory of Nonlinear Lattices, Springer Berlin, 1981.
[14] M. Toda, Nonlinear Waves and Solitons, Kluwer Dordrecht, 1983.
[15] V. A. Makarov, W. Ebeling, and M. G. Velarde, "Soliton-like waves
on dissipative Toda lattices", Int. J. Bifurcation and Chaos vol. 10, pp.
1075-1089, 2000.
[16] V. A. Makarov, E. Del Rio, W. Ebeling, and M. G. Velarde, "Dissipative
Toda-Rayleigh lattice and its oscillatory modes", Physical Review E vol.
64, pp. 036601-36615, 2001.
[17] E. Del Rio, V. A. Makarov, M. G. Velarde, and W. Ebeling, "Mode
transitions and wave propagation in a driven-dissipative Toda-Rayleigh
ring", Physical Review E vol. 67, pp. 056208-056217, 2003.
[18] S. Still, K. Hepp, and R. J. Douglas, "Neuromorphic walking gait
control", IEEE Trans. Neural Netw. vol 17, pp. 496-508, 2006.
[19] V. A. Makarov, M. G. Velarde, A. Chetverikov, and W. Ebeling,
"Anharmonicity and its significance to non-Ohmic electric conduction",
Physical Review E, vol. 73, pp. 066626-066612, 2006.
[20] Yu. A. Kuznetsov, Elements of Applied Bifurcation Theory, Springer-
Verlag, Berlin, 1995.
[21] A. C. Singer and A. V. Oppenheim, "Circuit implementation of soliton
systems", Int. J. Bifurcation Chaos vol. 9, pp. 571, 1999.
[22] N. Islam, J. P. Singh, and K. Steiglitz, "Soliton phase shifts in a
dissipative lattice", J. Appl. Phys. vol. 62, pp. 689-693, 1987.
@article{"International Journal of Electrical, Electronic and Communication Sciences:59765", author = "Valeri A. Makarov and Ezequiel Del Rio and Manuel G. Bedia and Manuel G. Velarde and Werner Ebeling", title = "Central Pattern Generator Incorporating the Actuator Dynamics for a Hexapod Robot", abstract = "We proposed the use of a Toda-Rayleigh ring as a
central pattern generator (CPG) for controlling hexapodal robots. We
show that the ring composed of six Toda-Rayleigh units coupled to
the limb actuators reproduces the most common hexapodal gaits. We
provide an electrical circuit implementation of the CPG and test our
theoretical results obtaining fixed gaits. Then we propose a method
of incorporation of the actuator (motor) dynamics in the CPG. With
this approach we close the loop CPG – environment – CPG, thus
obtaining a decentralized model for the leg control that does not
require higher level intervention to the CPG during locomotion in
a nonhomogeneous environments. The gaits generated by the novel
CPG are not fixed, but adapt to the current robot bahvior.", keywords = "Central pattern generator, electrical circuit, hexapod
robot", volume = "2", number = "3", pages = "472-6", }
